4 Astronomy Problems: ASSISTANCE NEEDED PLEASE

1. If a comet has an eccentricity of 0.98 and a semimajor axis of 12 AU, what are the apehlion and perihelion distances? What is the period? How does the velocity at perihelion compare to the velocity at aphelion?

In this problem, I used the perihelion and aphelion equations to solve for them, where P=(1-e)a and A=(1=e)a. Perihelion = 0.24 and Aphelion = 23.76. I don't know how to calcuate the velocity, and am confused by that. And since I have the eccentricity and semimajor axis, do I use the equation P(years) = R(A.U.)^3/2?

2. If this comet appeared to have a brightness of one at its nearest point to Earth, how bright would it appear at its maximum distance? Assume incorrectly that is does not change in luminosity as it approaches the Sun and use the inverse square law.

I know to use the inverse square law on this one, but how can I relate that to brightness and distances?

3. If an asteroid is in a 5:2 resonance with Jupiter, what is its semimajor axis?

The next two problems are the same and I don't have any equations for resonance but I will keep looking.

4. If an asteroid is in a 2:5 resonance with mars, what is its semimajor axis?

1. Your answers for app and per are correct. Notice how apphelion and perihelon values are just (sma x ecc) +/- sma. That's basically what your formula says too. For velocities, you could just say that velocity at perihelion is faster than velocity at aphelion, which is correct for any orbit. It doesn't actually tell you to compute it, just to compare it. Off the top of my head, I forget the formula. See if you can find it.

2. This question doesn't really make sense. What is it's nearest point to Earth? All we're given is its solar elements. This comet could have high inclination, meaning that it's nowhere near Earth's orbit as it passes the 1AU point in its orbit. It's closest point to Earth could be a brush with our outer atmosphere (~100km altitude, 6470 km distance). It's furthest point from Earth would be roughly its furthest point from the Sun, + 1AU.

3. What is this asteroid's period? You must first know Jupiter's peroid. How does semi-major axis relate to period? (Kepler's 3rd Law).

What are the dimensions of velocity? Are they distance, time, distance*time, distance/time? Are A.U. units of distance, time, temperature, etc? If you don't know the answer to these things, they can be found on the web or in your textbook.

2.) helio refers to: having the sun as the center?

"Perihelion" refers to the orbit's nearest point to the sun.

3,4) what do i do with the resonance?

What does it mean to be in resonance? For example, what does it mean to be in a 2:1 resonance?

1.) Most velocity = distance/time
the units should be km/s or m/s
using the equation you gave me for velocity: 2(pi)a/p * square root (1-e)/(1+e) doesn't have those units
the units for a = A.U.
the units for p = years
so that would leave me with A.U/years
distance/time
but that doesn't seem right? should i convert to kilometers and seconds?